Summary answer:
Leave MC installed on your primary drive. The program itself, and it's database (which we call the Library) only take up a few hundred MB. Very, very small by today's standards.
Your media files (songs, videos, etc) can be on any drive. If you have existing media in MC that you want to move to an external drive, you can easily do so using the Rename, Move, and Copy tool.
http://wiki.jriver.com/index.php/Rename,_Move,_and_Copy_FilesYou can also set up one or more locations on drives that you want monitored. We call this Auto Import. Set up a directory on an external drive for auto import, and MC will automatically pick up any media files you put there. You can do this for one drive, or for several drives.
https://wiki.jriver.com/index.php/Auto-Import...and of course, if you want to, you can manually import folders on any drive in your system.
Good luck!
Brian.